Geodesic
Totally real pseudo-umbilical submanifolds of a quaternion space form
Glasgow mathematical journal, Tome 40 (1998) no. 1, pp. 109-115

Voir la notice de l'article provenant de la source Cambridge University Press

Let M(c) denote a 4n-dimensional quaternion space form of quaternion sectional curvature c, and let P(H) denote the 4n-dimensional quaternion projective space of constant quaternion sectional curvature 4. Let N be an n-dimensional Riemannian manifold isometrically immersed in M(c). We call N a totally real submanifold of M(c) if each tangent 2-plane of N is mapped into a totally real plane in M (c). B. Y. Chen and C. S. Houh proved in [1]. 
Sun, Huafei. Totally real pseudo-umbilical submanifolds of a quaternion space form. Glasgow mathematical journal, Tome 40 (1998) no. 1, pp. 109-115. doi: 10.1017/S0017089500032390
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[1] 1.Chen, B. Y. and Houh, C. S., Totally real submanifolds of a quaternion projective space, Ann. di Math. Pura Appl. 120 (1979), 185–199. Google Scholar | DOI

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[3] 3.Chern, S. S., do Carmo, M. and Kobayashi, S., Minimal submanifolds of a sphere with second fundamental form of constant length, in Functional Analysis and Related Field (Springer-Verlag, New York, 1970) p. 60–75. Google Scholar

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